Unformatted text preview: ve that the price
is decreasing at a rate of $1.50 per PortaBoy sold. (Said diﬀerently, you can sell one more
PortaBoy for every $1.50 drop in price.) 4. To determine the price which will move 150 PortaBoys, we ﬁnd p(150) = −1.5(150)+250 = 25.
That is, the price would have to be $25. 5. If the price of a PortaBoy were set at $150, we have p(x) = 150, or, −1.5x+250 = 150. Solving,
we get −1.5x = −100 or x = 66.6. This means you would be able to sell 66 PortaBoys a week
if the price were $150 per system. Not all realworld phenomena can be modeled using linear functions. Nevertheless, it is possible to
use the concept of slope to help analyze nonlinear functions using the following:
Definition 2.3. Let f be a function deﬁned on the interval [a, b]. The average rate of change
of f over [a, b] is deﬁned as:
∆f
f (b) − f (a)
=
∆x
b−a
Geometrically, if we have the graph of y = f (x), the average rate of change over [a, b] is the slope of
the line which connects (a, f (a)) and (b, f (b)). This is called the sec...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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